An exit contract optimization problem

IF 1.3 3区数学 Q4 AUTOMATION & CONTROL SYSTEMS

Esaim-Control Optimisation and Calculus of Variations Pub Date : 2023-01-01 DOI:10.1051/cocv/2023064

Xihao He, Xiaolu Tan, Jun Zou

引用次数: 2

Abstract

We study an exit contract design problem, where one provides a universal exit contract to multiple heterogeneous agents, with which each agent chooses an optimal (exit) stopping time. The problem consists in optimizing the universal exit contract w.r.t. some criterion depending on the contract as well as the agents’ exit times. Under a technical monotonicity condition, and by using Bank-El Karoui’s representation of stochastic processes, we are able to transform the initial contract optimization problem into an optimal control problem. The latter is also equivalent to an optimal multiple stopping problem and the existence of the optimal contract is proved. We next show that the problem in the continuous-time setting can be approximated by a sequence of discrete-time ones, which would induce a natural numerical approximation method. We finally discuss the optimization problem over the class of all Markovian and/or continuous exit contracts.

查看原文本刊更多论文

一个退出契约优化问题

研究了一个退出契约设计问题，该问题为多个异构智能体提供了一个通用的退出契约，每个智能体选择一个最优的退出停止时间。问题在于根据契约和代理人的退出时间来优化通用退出契约。在技术单调性条件下，利用Bank-El Karoui的随机过程表示，我们能够将初始契约优化问题转化为最优控制问题。后者也等价于最优多次停车问题，并证明了最优契约的存在性。接下来，我们证明了连续时间设置下的问题可以用一系列离散时间的问题来逼近，这将推导出一个自然的数值逼近方法。最后讨论了所有马尔可夫和/或连续退出契约的优化问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Esaim-Control Optimisation and Calculus of Variations Mathematics-Computational Mathematics

自引率

7.10%

发文量

期刊介绍： ESAIM: COCV strives to publish rapidly and efficiently papers and surveys in the areas of Control, Optimisation and Calculus of Variations. Articles may be theoretical, computational, or both, and they will cover contemporary subjects with impact in forefront technology, biosciences, materials science, computer vision, continuum physics, decision sciences and other allied disciplines. Targeted topics include: in control: modeling, controllability, optimal control, stabilization, control design, hybrid control, robustness analysis, numerical and computational methods for control, stochastic or deterministic, continuous or discrete control systems, finite-dimensional or infinite-dimensional control systems, geometric control, quantum control, game theory; in optimisation: mathematical programming, large scale systems, stochastic optimisation, combinatorial optimisation, shape optimisation, convex or nonsmooth optimisation, inverse problems, interior point methods, duality methods, numerical methods, convergence and complexity, global optimisation, optimisation and dynamical systems, optimal transport, machine learning, image or signal analysis; in calculus of variations: variational methods for differential equations and Hamiltonian systems, variational inequalities; semicontinuity and convergence, existence and regularity of minimizers and critical points of functionals, relaxation; geometric problems and the use and development of geometric measure theory tools; problems involving randomness; viscosity solutions; numerical methods; homogenization, multiscale and singular perturbation problems.